Struggling with a Complex Partial Differential Equation: Can You Help?

In summary, the conversation discusses a partial differential equation and the person's difficulty in solving it. They share the equation and ask for help, and another person suggests a possible method of solving it using a change of variables. The original person then realizes they made a mistake and provides the correct equation.
  • #1
the_edge
2
0
Hello, I'm new at these equations so I need help. I'm not able to solve this partial differential equation, if there is somebody who can help me do it pleasez...

http://galeb.etf.bg.ac.yu/~ii030168d/problem/problem.GIF

OK, it begins like this:

http://galeb.etf.bg.ac.yu/~ii030168d/problem/problem1.GIF

But I don't know what to do next... This problem is from exam on my faculty. (I haven't pass)


I would appreciate any help...
 
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  • #2
Well, the first equation may be rewrittent as a ratio between the differentials of x and y as follows:
[tex]\frac{dy}{dx}=\frac{x-y-x^{2}y}{x+y+xy^{2}}[/tex]
I'm not sure if this is analytically solvable, though..
 
  • #3
You MIGHT try changing of variables u=x+y, v=x-y; possibly, that will simplify the expressions.
 
  • #4
Sorry I made a mistake, problem is next:

dx/(x+y-xy^2) = dy/(x^2y-x-y) = dz/(z(y^2-x^2))

Maybe now there is solution. Those changes can't help, they wouldn't simplify the expression, but thanks...
 
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FAQ: Struggling with a Complex Partial Differential Equation: Can You Help?

What is a partial differential equation (PDE)?

A PDE is a mathematical equation that involves multiple variables and their partial derivatives. It describes how a quantity changes over time and space, and is often used to model complex physical phenomena in fields such as physics, engineering, and finance.

Why are PDEs difficult to solve?

PDEs are difficult to solve because they involve multiple variables and their derivatives, making them more complex than ordinary differential equations. They also lack analytical solutions, so numerical methods must be used, which can be time-consuming and computationally intensive.

What are some common techniques for solving PDEs?

Some common techniques for solving PDEs include separation of variables, the method of characteristics, finite difference methods, and finite element methods. Each method has its own strengths and limitations, and the choice of technique depends on the specific problem being solved.

How do boundary conditions and initial conditions affect the solution of a PDE?

Boundary conditions and initial conditions are essential in solving PDEs as they provide information about the behavior of the solution at the boundaries and initial time, respectively. Without these conditions, the PDE may have multiple solutions or no solution at all.

Can PDEs be solved analytically?

In general, PDEs cannot be solved analytically, meaning that there is no closed-form solution that can be written down. However, for simple PDEs, analytical solutions may exist. In most cases, numerical methods must be used to approximate the solution of a PDE.

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